Wikipedia wrote:Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

1 = 12 = 103 = 1004 = 1015 = 10006 = ...?

Just for reference, and those unfamiliar with the Fibonacci sequence who want to play, the first few Fibonacci numbers are:

That's right, a-wan. Basically the way I see it, what's going to go on here is we're gonna pretend like we're translating Zeckendorf's representation into a base system that resembles binary, in that it will contain only ones and zeros. The Fibonacci numbers will be our "orders of magnitude" or place values: from the rightmost digit, just go in your head, "1, 2, 3, 5, 8, 13, 21, 34, 55, etc..."

Eh.. maybe. I dunno actually, because the answer I was looking for technically has little if anything to do with the Zeckendorf's representation. It has more to do with another thing that I came up with, but I never was sure what I should call it...

I've never actually written this stuff out before (and now I guess I shouldn't have to ) so I just realized another thing that's going on here: if someone came along one day and said, "I want to create a base system that only has two symbols (1 and 0), but let's say that numbers can only be written in such a way that the 1s never touch eachother..." This is also what you would come up with.